A156181 Number of solutions to e(1)*1 + e(2)*2 + ... + e(n)*n = e(-1)*1 + e(-2)*2 + ... + e(-n)*n, where e(j) are from {-1,0,1}, j=-n,...,n.

1, 3, 13, 65, 403, 2669, 18759, 136477, 1020373, 7785741, 60395165, 474817833, 3775005799, 30298719855, 245167429681, 1997854542163, 16381233095985, 135050690760831, 1118800428892925, 9308791880014333, 77755512086256649

Offset

0,2

Comments

a(n) = coefficient of x^(n*(n+1)) in the polynomial Product_{k=1..n} (1 + x^k + x^(2*k))^2, and is the maximal such coefficient as well.

Links

Ray Chandler, Table of n, a(n) for n = 0..1052 (terms < 10^1000)

Steven R. Finch, Signum equations and extremal coefficients, February 7, 2009. [Cached copy, with permission of the author]

Formula

a(n) is the constant term in expansion of Product_{k=1..n} (x^k + 1 + 1/x^k)^2. - Ilya Gutkovskiy, Jan 22 2024

Mathematica

Table[Coefficient[Expand[Product[(1 + x^k + x^(2*k))^2, {k, 1, n}]], x, n*(n + 1)], {n, 0, 20}]

Crossrefs

Cf. A007576, A047653, A063865.

Sequence in context: A199143 A002468 A198663 * A260783 A228987 A112807

Adjacent sequences: A156178 A156179 A156180 * A156182 A156183 A156184

Keyword

nonn

Author

Steven Finch, Feb 05 2009

Status

approved